Question

How is magnetic flux calculated?

Answer 1

Magnetic flux (
Φ
Φ) is a measure of the total magnetic field passing through a surface. It is a scalar quantity and is usually measured in units of weber (Wb), which is equivalent to volts-seconds (V·s). The magnetic flux through a surface can be calculated using the following formula:

Φ
=

⋅

⋅
cos
⁡
(

)
Φ=B⋅A⋅cos(θ),

where:

Φ
Φ is the magnetic flux through the surface,

B is the magnetic field strength perpendicular to the surface (measured in teslas, T),

A is the area of the surface that the magnetic field passes through (measured in square meters, m²),

θ is the angle between the magnetic field direction and the normal to the surface.

If the magnetic field is uniform (i.e., it has a constant magnitude and direction) over the entire surface, then the formula simplifies to:

Φ
=

⋅

Φ=B⋅A,

since
cos
⁡
(
0
°
)
=
1
cos(0°)=1 (when the magnetic field is perpendicular to the surface) and
cos
⁡
(
90
°
)
=
0
cos(90°)=0 (when the magnetic field is parallel to the surface).

If the magnetic field is not uniform and varies across the surface, the flux can be calculated by integrating the product of the magnetic field and the differential area (


dA) over the surface:

Φ
=
∫

⋅


Φ=∫B⋅dA,

where

B is the magnetic field vector and


dA is a differential area vector.

In summary, the magnetic flux through a surface is determined by the strength of the magnetic field, the area of the surface, and the angle between the magnetic field direction and the surface normal.